Hey the server (DMU) crashed (I think), and now on the website it says 'Public 1.16.5' however I can't join the server.

It gives me the message 'Failed to synchronize registry data from server, closing connection.

Is this a problem from my side or the server's side?

You'll need to download and install the new update

https://www.curseforge.com/minecraft/mc-mods/the-dalek-mod/files/4258146